Precalculus - Pearson

A Correlation of

to the

South Carolina Academic Standards for Mathematics Precalculus

Precalculus, 4th Edition (Blitzer) © 2010 to the South Carolina Academic Standards for Mathematics Precalculus INTRODUCTION This document demonstrates how Precalculus (Blitzer), 4th Edition © 2010, meets the indicators of the South Carolina Academic Standards for Mathematics Precalculus. Correlation page references are to the Student Edition and Instructor’s Edition Manual and are cited at the page level. Blitzer creates intriguing applications that show students the relevance of math. Appealing to a wide range of interests and majors, the program’s applications captivate students’ imagination with his passion for integrating math into the worlds of contemporary society, culture, art, and science. Features: •

Clear and accessible presentation ensures that students can follow the book when they get home from class. o

Voice balloons offer the support and guidance of a teacher’s voice. These specific annotations clarify procedures and concepts, mimicking what a teacher would say in class when translating the math into plain English.

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See it, Hear it, Try it is the consistent format of every textbook example.

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Extensive exercise sets at the end of each section are organized into six categories: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Group Exercises. This variety lets teachers create well-rounded homework assignments, while holding students’ interest with an ongoing selection of novel applications. Practice Plus Problems are more challenging problems that test conceptual understanding by requiring students to combine skills and to revisit key concepts in order to solve.

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New to this edition are Make Sense? Classroom discussion exercises that contain four critical thinking problems that test for conceptual understanding. This is an opportunity for students to express their opinions and for teachers to provide feedback on those thoughts.

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Assessment includes Mid-Chapter Checkpoints, Cumulative Review Exercises at the end of each chapter, and End-of-chapter tests. These ensure that students remember previously learned material, keeping the fundamental skills and concepts fresh in their minds.

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Integrated study aids help students make the most of their time outside of the classroom. o

Chapter Test Prep Videos (included with the Student Edition) contain worked-out solutions to every exercise in every chapter test. A teacher walks students through all examples step-by-step, allowing students to pause and watch again as needed.

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Study Tip boxes appear throughout the book. These offer suggestions for problem solving, point out common student errors, and provide informal tips and suggestions.

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Technology boxes illustrate the many capabilities of graphing utilities that go beyond just graphing.

This document demonstrates the success students will achieve by using Precalculus by Blitzer.

2 SE = Student Edition

TE = Teacher’s Edition

Precalculus, 4th Edition (Blitzer) © 2010 to the South Carolina Academic Standards for Mathematics Precalculus Precalculus, 4th Edition (Blitzer) © 2010

Indicators

Standard PC-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. PC-1.1 Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

SE/TE: 128 (#124-#131), 202 (#33-#38), 251 (#75-#82), 300 (#77-#82), 325 (#57-#64), 337 (#65-#71), 357-358 (#102-#110), 378 (#40-#47), 399 (#77-#80), 412 (#120-#127), 422 (#105-#112), 450 (#59-#67), 535 (#89#97), 576 (#63-#69), 595 (#75-#78)

PC-1.2 Connect algebra and trigonometry with other branches of mathematics.

SE/TE: 54, 55, 66, 68, 81, 102-108, 187-188, 246-249, 259-260, 297, 302, 409, 444-445, 475-488, 489-501

PC-1.3 Apply algebraic methods to solve problems in real-world contexts.

SE/TE: 187-188, 189-191, 293-297, 299-300, 352-354, 356-357, 364-366, 369-376, 377-378, 394-396, 398-399, 407-408, 411-412, 430-432, 433-435

PC-1.4 Judge the reasonableness of mathematical solutions.

SE/TE: 103, 105, 107, 108, 109, 110, 125, 427, 738, 739, 751, 752, 769, 770, 774

PC-1.5 Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

SE/TE: 147-163, 164-177, 187-188, 204-219, 252-266, 286-301, 302-315, 340-358, 369-378, 423-435, 436-451, 515-536, 537-549, 736741,773-774

PC-1.6 Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

SE/TE: 148-150, 187, 257-259, 365, 373, 443445, 532, 568, 570, 571, 651, 656, 659, 660, 783

PC-1.7 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

SE/TE: 139-140, 152, 154, 247, 257, 307, 420, 485-486, 532, 558, 587, 634-635, 669, 731, 920

Standard PC-2: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions. PC-2.1 Carry out a procedure to graph parent functions (including y = xn, y = loga x, y = ln x, y =

SE/TE: 341-343, 389-391, 393-394, 403-406, 515-529, 537-544, 545

1 , y = ex, y = ax, y = sin x, y = cos x

x, y = tan x, y = csc x, y = sec x, and y = cot x).

SE = Student Edition

3



Indicators PC-2.2 Carry out a procedure to graph transformations (including –f(x), a • f(x), f(x) + d, f(x - c), f(-x), f(b • x), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

SE/TE: 204-219, 346-347, 392-393, 405-406, 408-409, 517-525, 526-530, 539-542, 543-544

PC-2.3 Analyze a graph to describe the transformation (including –f(x), a • f(x), f(x) + d, f(x - c), f(-x), f(b • x), |f(x)|, and f(|x|)) of parent functions.

SE/TE: 204-219, 346-347, 392-393, 405-406, 408-409, 517-525, 526-530, 539-542, 543-544

PC-2.4 Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y

SE/TE: 86-87, 98, 423-430, 432, 433, 626-639, 641

= xn, y = loga x, y = ln x, y =

1 , x

y = ex, y = ax, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x). SE/TE: 340-434, 406-407, 411, 478, 479, 517, 526, 538, 541, 542, 543, 545

PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = xn, y = loga x, y = ln x, y=

1 , y = ex, y = ax, y = sin x, y = cos x, y = x

tan x, y = csc x, y = sec x, and y = cot x). PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.

SE/TE: 167-169, 205, 480-481, 517, 526, 537, 538, 541, 542, 543

PC-2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

SE/TE: 159, 164-167, 257, 258, 259, 271, 286295, 298, 299, 306-311, 326-335, 389-391, 404-406, 517-536, 537-549

PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.

SE/TE: 235-239, 240-243, 273-274, 550-558, 400-405

PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.

SE/TE: 235-239, 240-243, 273-274, 550-558, 400-405

Standard PC-3: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions. SE/TE: 286-292, 298, 303-306, 307, 308, 309, 310-311, 312, 313, 315, 380, 382

PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.


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Indicators PC-3.2 Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

SE/TE: 327-332, 335, 336, 380, 383, 386

PC-3.3 Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

SE/TE: 327-332, 335, 336, 386

PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

SE/TE: 340-358, 381, 383

PC-3.5 polynomial situation. PC-3.6 polynomial

Analyze given information to write a function that models a given problem

SE/TE: 293, 295, 296, 297, 299, 316, 325,337, 339

Carry out a procedure to solve equations algebraically.

SE/TE: 323, 324, 325, 326, 330-332, 336, 339, 383, 386

PC-3.7 Carry out a procedure to solve polynomial equations graphically.

SE/TE: 306-307, 310-311, 323, 324, 325, 328, 330, 333, 385, 386

PC-3.8 Carry out a procedure to solve rational equations algebraically.

SE/TE: 86-87, 98, 131

PC-3.9 Carry out a procedure to solve rational equations graphically.

SE/TE: 347-351, 355, 386

PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.

SE/TE: 360-362, 366, 384, 386

PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

SE/TE: 359, 361, 362, 366, 384, 386

Standard PC-4: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions. PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

SE/TE: 389-399, 423, 453, 454

PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

SE/TE: 404-412, 423, 454

PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

SE/TE: 388-399, 423, 453, 454

PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

SE/TE: 400-412, 423, 454


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Indicators PC-4.5 Apply the laws of exponents to solve problems involving rational exponents.

SE/TE: 19-22, 39-42, 43, 44, 45, 129, 131, 133

PC-4.6 Analyze given information to write an exponential function that models a given problem situation.

SE/TE: 394-396, 397, 398, 399, 436-451, 456

PC-4.7 Apply the laws of logarithms to solve problems.

SE/TE: 414-419, 421, 423, 454, 457

PC-4.8 Carry out a procedure exponential equations algebraically.

to

solve

SE/TE: 423-427, 431, 432, 433, 455

PC-4.9 Carry out a procedure exponential equations graphically.

to

solve

SE/TE: 424, 427, 430, 435, 443

PC-4.10 Carry out a procedure logarithmic equations algebraically.

to

solve

SE/TE: 427-430, 432, 433, 455, 457, 458

PC-4.11 Carry out a procedure logarithmic equations graphically.

to

solve

SE/TE: 428, 433, 435, 455, 457, 458

Standard PC-5: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions. PC-5.1 Understand how angles are measured in either degrees or radians.

SE/TE: 460-464, 473, 580, 583

PC-5.2 Carry out a procedure to convert between degree and radian measures.

SE/TE: 463-464, 514, 580, 583

PC-5.3 Carry out a procedure to plot points in the polar coordinate system.

SE/TE: 664-667, 672, 673, 685, 724

PC-5.4 Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

SE/TE: 515-536, 537-549, 581, 582

PC-5.5 Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes).

SE/TE: 515-536, 537-549, 581, 582

PC-5.6 Apply a procedure to evaluate trigonometric expressions.

SE/TE: 487, 513, 515, 560-562, 563, 581, 582 583, 598, 603, 604, 609, 615, 623

PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.

SE/TE: 483, 488, 531, 532, 534, 535, 536, 547, 548, 549


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Indicators PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.

SE/TE: 495-498, 499, 500, 501, 581

PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.

SE/TE: 650, 653, 721, 723

PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.

SE/TE: 626-635, 636, 637

PC-5.11 Carry out a procedure to solve trigonometric equations graphically.

SE/TE: 626, 628, 629, 633, 637

PC-5.12 Apply the laws of sines and cosines to solve problems.

SE/TE: 644-655, 656-664, 721, 723, A2-A3

PC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangent.

SE/TE: 550-552, 553-554, 555-557, 563

PC-5.14 Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

SE/TE: 480-483, 487, 586, 596-618, 619-625, 633, 639, 640, 641, 642

PC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

See prerequisite concepts and skills. SE/TE: 178-180, 188, 271, 495-497, 500 (#66)

Standard PC-6: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically. PC-6.1 Carry out a procedure to graph the circle whose equation is the form

SE/TE: 246-249, 250, 251, 252, 274

PC-6.2 Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

SE/TE: 246, 247, 250, 274

PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.

SE/TE: 769-770, 774, 775, 777, 801, 802

PC-6.4 Carry out a procedure to graph the ellipse whose equation is the form

SE/TE: 874-885, 912, 946

(x − h) 2 + (y − k) 2 = r 2 .

(x − h )

2

a2

(y − k ) +

2

b2

= 1.


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Indicators PC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form

(x − h)2 ( y − k )2 a2

−

b2

SE/TE: 886-900, 912, 946

= 1. SE/TE: 900-911, 912, 947

PC-6.6 Carry out a procedure to graph the parabola whose equation is the form

y − k = a(x − h) 2 .


8
